Edge & Adjacent
These two points requested to be called vertices.
Now the two vertices are isolated points of a Graph. They are not connected. A graph no needs to be connected. A graph that is not connected, of course it is called a disconnected graph.
From these two vertices, an arc line was born, and the name of the arc is an edge .
Now the two vertices are connected. The arc is connecting the two points.
Because they are connected, the two vertices are now called adjacent or neighbors .
Like a little baby, an edge cannot exist alone without at least one vertex to support it. If there is no vertex, the edge does not exist.
However, an edge cannot be supported by more than two vertices.
Teknomo, Kardi (2015) Pictorial Introduction to Graph Theory. http:\\people.revoledu.com\kardi\tutorial\GraphTheory\